`BookProof.ChapterObservableExpectation.attention_mem_convexHull` (q : EuclideanSpace ℝ (Fin n)) (k : Fin m → EuclideanSpace ℝ (Fin n)) (v : Fin m → E) (j₀ : Fin m) : attentionOutp

Proved

BookProof.ChapterObservableExpectation.attention_mem_convexHull

by leonardopedro · Oct 10, 2026 · Mathlib 0df444a (Lean v4.33.1)

theoremstimepiece

Prove the following Lean 4 theorem from ChapterObservableExpectation.

BookProof.ChapterObservableExpectation.attention_mem_convexHull (q : EuclideanSpace ℝ (Fin n)) (k : Fin m → EuclideanSpace ℝ (Fin n)) (v : Fin m → E) (j₀ : Fin m) : attentionOutput q k v ∈ convexHull ℝ (Set.range v)

Formalization note: Lean 4 identifier BookProof.ChapterObservableExpectation.attention_mem_convexHull.

Preamble

-- Generated from ChapterObservableExpectation.lean — theorem BookProof.ChapterObservableExpectation.attention_mem_convexHull
import Mathlib
import Definitions.Def_ChapterObservableExpectation
import Definitions.Def_ChapterSoftmaxBorn
open BookProof.ChapterSoftmaxBorn
open BookProof.ChapterObservableExpectation


open scoped BigOperators

noncomputable section


open BookProof.ChapterSoftmaxBorn

variable {m n : ℕ}
variable {E : Type*} [AddCommGroup E] [Module ℝ E]

Formal statement

theorem BookProof.ChapterObservableExpectation.attention_mem_convexHull (q : EuclideanSpace ℝ (Fin n))
    (k : Fin m → EuclideanSpace ℝ (Fin n)) (v : Fin m → E) (j₀ : Fin m) :
    attentionOutput q k v ∈ convexHull ℝ (Set.range v) := by sorry

View graph